The present ratio of ages of P and Q is 2 : 7. Six years ago, this ratio was 1 : 5. Determine the present age of P?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 16 years
The present ratio 2 : 7 lets both ages be written with one unknown. Six years ago each age was 6 less, and the old ratio 1 : 5 then gives an equation for it.
Present ages: P \(=2x\), Q \(=7x\)
Six years ago: \(\displaystyle \frac{2x-6}{7x-6}=\frac{1}{5}\)
\(10x-30=7x-6\)
\(3x=24\), so \(x=8\)
P\(=2\times8=16\) years